Puerto Rico’s governor, saying he needs to pull the island out of a “death spiral,” has concluded that the commonwealth cannot pay its roughly $72 billion in debts, an admission that will probably have wide-reaching financial repercussions.

The governor, Alejandro García Padilla, and senior members of his staff said in an interview last week that they would probably seek significant concessions from as many as all of the island’s creditors, which could include deferring some debt payments for as long as five years or extending the timetable for repayment.

“The debt is not payable,” Mr. García Padilla said. “There is no other option. I would love to have an easier option. This is not politics, this is math.”

It is a startling admission from the governor of an island of 3.6 million people, which has piled on more municipal bond debt per capita than any American state.

A broad restructuring by Puerto Rico sets the stage for an unprecedented test of the United States municipal bond market, which cities and states rely on to pay for their most basic needs, like road construction and public hospitals.

That market has already been shaken by municipal bankruptcies in Detroit; Stockton, Calif.; and elsewhere, which undercut assumptions that local governments in the United States would always pay back their debt.

Puerto Rico’s bonds have a face value roughly eight times that of Detroit’s bonds. Its call for debt relief on such a vast scale could raise borrowing costs for other local governments as investors become more wary of lending.

Perhaps more important, much of Puerto Rico’s debt is widely held by individual investors on the United States mainland, in mutual funds or other investment accounts, and they may not be aware of it.

Puerto Rico, as a commonwealth, does not have the option of bankruptcy. A default on its debts would most likely leave the island, its creditors and its residents in a legal and financial limbo that, like the debt crisis in Greece, could take years to sort out.

Still, Mr. García Padilla said that his government could not continue to borrow money to address budget deficits while asking its residents, already struggling with high rates of poverty and crime, to shoulder most of the burden through tax increases and pension cuts.

He said creditors must now “share the sacrifices” that he has imposed on the island’s residents.

“If they don’t come to the table, it will be bad for them,” said Mr. García Padilla, who plans to speak about the fiscal crisis in a televised address to Puerto Rico residents on Monday evening. “What will happen is that our economy will get into a worse situation and we’ll have less money to pay them. They will be shooting themselves in the foot.”

With some creditors, the restructuring process is already underway. Late last week, Puerto Rico officials and creditors of the island’s electric power authority were close to a deal that would avoid a default on a $416 million payment due on Wednesday.

With other payment deadlines looming, Mr. García Padilla and his staff said they would begin looking for possible concessions on all forms of government debt.

The central government must set aside about $93 million each month to pay its general obligation bonds — a crucial action in Puerto Rico because its constitution requires such bonds to be paid before any other expense. No American state has restructured its general obligation debt in living memory.

The government’s Public Finance Corporation, which has issued bonds to finance budget deficits in the past, owes $94 million on July 15. The Government Development Bank — the commonwealth’s fiscal agent — must repay $140 million of bond principal by Aug. 1.

“My administration is doing everything not to default,” Mr. García Padilla said. “But we have to make the economy grow,” he added. “If not, we will be in a death spiral.”

A proposed debt exchange, where creditors would replace their current debt with new bonds with terms more favorable to Puerto Rico, signals a significant shift for Mr. García Padilla, a member of the Popular Democratic Party, who was elected in 2012. His party is aligned with the Democrats on the mainland and favors maintaining the island’s legal status as a commonwealth.

He said that when he took office, he tried to balance the fiscal situation through austerity measures and fresh borrowing. But he saw that the island was caught in a vicious circle where it borrowed to balance the budget, raised the debt and had an even bigger budget deficit the next year.

Residents began leaving for the mainland in droves, and Puerto Rico’s credit was downgraded to junk, making borrowing extremely expensive.

Only a few months ago, the administration was considering borrowing as much as an additional $2.9 billion, which would be paid for by a fuel tax.

But recently, Mr. García Padilla’s team has been laying the groundwork for more drastic action. The governor commissioned a study of the financial situation by former officials at the International Monetary Fund and the World Bank. Concluding that the debt load is unsustainable, the report suggests a bond exchange, with the new bonds carrying “a longer/lower debt service profile,” according to a confidential copy reviewed by The New York Times. The García Padilla administration made the report public on Monday.

“There is no U.S. precedent for anything of this scale or scope,” according to the report, one of whose writers was Anne O. Krueger, a former chief economist at the World Bank and currently a research professor at the School of Advanced International Studies at Johns Hopkins University.

The “Krueger Report,” as it is being called, also seems aimed at the Obama administration and Congress, both of which have taken a largely hands-off approach to Puerto Rico’s fiscal problems. United States Treasury officials, however, have been advising the island’s government in recent months amid the worsening fiscal situation.

In June, Puerto Rico hired Steven W. Rhodes, the retired federal judge who oversaw Detroit’s bankruptcy case, as an adviser. The government is also consulting with a group of bankers from Citigroup who advised Detroit on a $1.5 billion debt exchange with certain creditors.

In Washington, the García Padilla administration has been pushing for a bill that would allow the island’s public corporations, like its electrical power authority and water agency, to declare bankruptcy. Of Puerto Rico’s $72 billion in bonds, roughly $25 billion were issued by the public corporations.

Some officials and advisers say Congress needs to go further and permit Puerto Rico’s central government to file for bankruptcy — or risk chaos.

“There are way too many creditors and way too many kinds of debt,” Mr. Rhodes said in an interview. “They need Chapter 9 for the whole commonwealth.”

Hedge funds holding billions of dollars of the island’s bonds at steep discounts are frustrated that the government has not seemed willing to reach a deal to borrow more money from them.

“We want to be a part of the solution to the commonwealth’s fiscal challenges,” a group of investment firms, including Centerbridge Partners and Monarch Alternative Capital, wrote in a letter last week.

An aide to the governor said the hedge funds’ debt proposal was too onerous. And the deal would only postpone Puerto Rico’s inevitable reckoning.